Origami

Essentially, origami is the art of folding paper. The purpose of this art is to create works by using the scheme of geometric folds. The term origami refers to all types of folding paper. Origami uses a few different folds, but they can be combined in many ways and form very complex shapes. Usually, origami figures are made without cuts from a square sheet, the sides of which can be different colors. While being a simple and basic form of self-entertainment, the philosophy of origami goes beyond that and can take a form of art, intellectual stimulation, and meditation.

Peculiarities of the Origami Art

Although there are some differences in the origin of origami, it is safe to say that origami developed in Japan. At first, it was a toy mainly for children. Since the 1960s, the art of origami has been actively spread around the world, there are such areas as modular origami, kirigami, and pure origami. The largest example of origami is a paper boat that can withstand the weight of several people (Hinders). Thus, origami is not merely paper folding, it is a form of art that can be manifested in a variety of ways allowing an artist to express themselves at the top of their capabilities.

Although any sheet material can be used for origami, the choice of material greatly affects the assembly and final appearance of the model. Here are some features of origami paper:

• Plain copy paper with a density of 70-90 g/m2 can be used for simple models such as a crane.
• Heavier paper with a density of more than 100 g/m2 is usually used by wet folding technology. This technology allows you to create rounded models that become hard and durable when dry.
• Special origami paper, called kami, is sold in squares of different sizes from 2.5 cm to 25 cm and larger.
• Usually, this paper has white and colored sides. But also use paper that is colored or patterned on both sides.
• Usually origami paper has a lower density than copy paper, which allows you to create more complex models.
• For complex models in origami use foil paper - glued together very thin sheets of foil and paper.
• Also, take foil fabric - glued thin sheets of kitchen aluminum foil and fabric.
• Even use a "sandwich" with layers of fabric/foil/fabric.

Specific types of paper, such as anru, elbow, hanzi, gampi, goat, saa have long fibers and are usually very strong. Because such paper must first be flexible, it is often covered or primed with methylcellulose or wheat paste. This paper is extremely thin, so it allows you to make the smallest folds, such as in the limbs of insect models (“Origami Folding Techniques to Master”). Due to the diversity of materials and techniques, origami is a form of art accessible to anyone who has access to paper.

Mathematics and Origami

The practice and study of origami relate to some areas of mathematics. The problem of flat bending raises the question of whether it is possible to bend the specimen into a two-dimensional model. Importantly, the paper shows zero Gaussian curvature at all points on the surface. Only the folds are lines of zero curvature. But the curvature along the surface of the unbent folds on wet paper or folds of the nail does not satisfy this condition (Lazarus, Smith, and Dickey). This sounds somewhat complex, yet the practical manifestation of such math is not overly complicated or unimaginable. Essentially, the math of origami is mostly about the bend angles and their interaction within the same surface.

The problem of solid origami has some practical significance. It is formulated as follows - if we replace the paper with a sheet of metal and use rods instead of fold lines, will we be able to get the right model? An example of a solution to this problem is the rigid folds of the Miura map, which are used to deploy solar panels for space satellites (Hull). It is quite clear that origami is a multi-dimanesional discipline that contributes not only to math or art but also to such important and relevant disciplines as sustainable energy.

Conclusion

The amazing thing is the ability to fold paper into recognizable figures without the help of aids (glue, scissors). You should not look for an easy way, you should look for solutions, harmony, beauty, meaning. At the same time, you solve a geometric problem, even if you are not trained in these sciences. During the compilation, you are a meditating philosopher, a patient seeker, a whole person who is able to create and give a creative part of his soul. You are very close to understanding the fragility of all things, and because of this to comprehend eternity, the essence of life.

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Works Cited

"Origami Folding Techniques To Master". Discount Art N Craft Warehouse, 2022, https://discountartncraftwarehouse.com.au/blog-2138/origami-folding-techniques-to-master.

Hinders, Dana. "Express Your Creativity And Develop Math Skills By Learning Origami". The Spruce Crafts, 2019, https://www.thesprucecrafts.com/brief-history-of-origami-2540653.

Hull, Thomas C. "Miura Map Folding And Unfolding". Wolfram Demonstrations Project, 2011, https://demonstrations.wolfram.com/MiuraMapFoldingAndUnfolding/.

Lazarus, Nathan et al. "Self‐Folding Metal Origami". Advanced Intelligent Systems, vol 1, no. 7, 2019, p. 1900059. Wiley, https://doi.org/10.1002/aisy.201900059. Accessed 7 Mar 2022.